General Solutions to Functional and Kinematic Redundancy

A systematic and general approach to represent functional redundancy is presented. It is shown how this approach allows the freedom provided by functional redundancy to be integrated into the inverse geometric problem for real-time applications and how it can be utilised to improve performance. A set of new iterative solutions to the inverse geometric problem, well suited for kinematically redundant manipulators, is also presented

Kinematically redundant robot manipulators

Research on control, design and programming of kinematically redundant robot manipulators (KRRM) is discussed. These are devices in which there are more joint space degrees of freedom than are required to achieve every position and orientation of the end-effector necessary for a given task in a given workspace. The technological developments described here deal with: kinematic programming techniques for automatically generating joint-space trajectories to execute prescribed tasks; control of redundant manipulators to optimize dynamic criteria (e.g., applications of forces and moments at the end-effector that optimally distribute the loading of actuators); and design of KRRMs to optimize functionality in congested work environments or to achieve other goals unattainable with non-redundant manipulators. Kinematic programming techniques are discussed, which show that some pseudo-inverse techniques that have been proposed for redundant manipulator control fail to achieve the goals of avoiding kinematic singularities and also generating closed joint-space paths corresponding to close paths of the end effector in the workspace. The extended Jacobian is proposed as an alternative to pseudo-inverse techniques

Asymmetric Dual-Arm Task Execution using an Extended Relative Jacobian

Coordinated dual-arm manipulation tasks can be broadly characterized as possessing absolute and relative motion components. Relative motion tasks, in particular, are inherently redundant in the way they can be distributed between end-effectors. In this work, we analyse cooperative manipulation in terms of the asymmetric resolution of relative motion tasks. We discuss how existing approaches enable the asymmetric execution of a relative motion task, and show how an asymmetric relative motion space can be defined. We leverage this result to propose an extended relative Jacobian to model the cooperative system, which allows a user to set a concrete degree of asymmetry in the task execution. This is achieved without the need for prescribing an absolute motion target. Instead, the absolute motion remains available as a functional redundancy to the system. We illustrate the properties of our proposed Jacobian through numerical simulations of a novel differential Inverse Kinematics algorithm.Comment: Accepted for presentation at ISRR19. 16 Page

Computational neural learning formalisms for manipulator inverse kinematics

An efficient, adaptive neural learning paradigm for addressing the inverse kinematics of redundant manipulators is presented. The proposed methodology exploits the infinite local stability of terminal attractors - a new class of mathematical constructs which provide unique information processing capabilities to artificial neural systems. For robotic applications, synaptic elements of such networks can rapidly acquire the kinematic invariances embedded within the presented samples. Subsequently, joint-space configurations, required to follow arbitrary end-effector trajectories, can readily be computed. In a significant departure from prior neuromorphic learning algorithms, this methodology provides mechanisms for incorporating an in-training skew to handle kinematics and environmental constraints

Collision-free inverse kinematics of the redundant seven-link manipulator used in a cucumber picking robot

The paper presents results of research on an inverse kinematics algorithm that has been used in a functional model of a cucumber-harvesting robot consisting of a redundant P6R manipulator. Within a first generic approach, the inverse kinematics problem was reformulated as a non-linear programming problem and solved with a Genetic Algorithm (GA). Although solutions were easily obtained, the considerable calculation time needed to solve the problem prevented on-line implementation. To circumvent this problem, a second, less generic, approach was developed which consisted of a mixed numerical-analytic solution of the inverse kinematics problem exploiting the particular structure of the P6R manipulator. Using the latter approach, calculation time was considerably reduced. During the early stages of the cucumber-harvesting project, this inverse kinematics algorithm was used off-line to evaluate the ability of the robot to harvest cucumbers using 3D-information obtained from a cucumber crop in a real greenhouse. Thereafter, the algorithm was employed successfully in a functional model of the cucumber harvester to determine if cucumbers were hanging within the reachable workspace of the robot and to determine a collision-free harvest posture to be used for motion control of the manipulator during harvesting. The inverse kinematics algorithm is presented and demonstrated with some illustrative examples of cucumber harvesting, both off-line during the design phase as well as on-line during a field test

Characterization and control of self-motions in redundant manipulators

The presence of redundant degrees of freedom in a manipulator structure leads to a physical phenomenon known as a self-motion, which is a continuous motion of the manipulator joints that leaves the end-effector motionless. In the first part of the paper, a global manifold mapping reformulation of manipulator kinematics is reviewed, and the inverse kinematic solution for redundant manipulators is developed in terms of self-motion manifolds. Global characterizations of the self-motion manifolds in terms of their number, geometry, homotopy class, and null space are reviewed using examples. Much previous work in redundant manipulator control has been concerned with the redundancy resolution problem, in which methods are developed to determine, or resolve, the motion of the joints in order to achieve end-effector trajectory control while optimizing additional objective functions. Redundancy resolution problems can be equivalently posed as the control of self-motions. Alternatives for redundancy resolution are briefly discussed

A hyper-redundant manipulator

“Hyper-redundant” manipulators have a very large number of actuatable degrees of freedom. The benefits of hyper-redundant robots include the ability to avoid obstacles, increased robustness with respect to mechanical failure, and the ability to perform new forms of robot locomotion and grasping. The authors examine hyper-redundant manipulator design criteria and the physical implementation of one particular design: a variable geometry truss

Handling robot constraints within a Set-Based Multi-Task Priority Inverse Kinematics Framework

Set-Based Multi-Task Priority is a recent framework to handle inverse kinematics for redundant structures. Both equality tasks, i.e., control objectives to be driven to a desired value, and set-bases tasks, i.e., control objectives to be satisfied with a set/range of values can be addressed in a rigorous manner within a priority framework. In addition, optimization tasks, driven by the gradient of a proper function, may be considered as well, usually as lower priority tasks. In this paper the proper design of the tasks, their priority and the use of a Set-Based Multi-Task Priority framework is proposed in order to handle several constraints simultaneously in real-time. It is shown that safety related tasks such as, e.g., joint limits or kinematic singularity, may be properly handled by consider them both at an higher priority as set-based task and at a lower within a proper optimization functional. Experimental results on a 7DOF Jaco$^2